A conventional interferometric measuring device is described in the publication, T. Dresel, G. Hausler, H. Venzke "Three-Dimensional Sensing of Rough Surfaces by Coherence Radar", App. Opt., vol. 31, no. 7 of Mar. 1, 1992. This publication proposes using an interferometer having a light source that is coherent over a short distance and a piezoelectrically driven reflector to measure the profile of rough surfaces. In the measuring device, a first beam component, in the form of reference wave, is superimposed on another beam component, in the form of a measuring beam, which is reflected off of a test object. The two light waves have a very short coherence length (a few .mu.m), so that the interference contrast reaches a maximum when the optical path difference is zero. To change the path of light of the reference wave, the reflecting element is provided in the form of the piezoelectrically driven reflector. The distance to the test object is able to be determined by comparing the position of the piezoelectrically driven reflector to the time of occurrence of the interference maximum. In this context, difficulties can arise when precisely determining the interference maximum and its association to the path of light, since uniquely defining the position of the piezoelectrically driven reflector entails substantial outlay.